Anisotropic diffusion filtering applied to individual PET activation images: a simulation study

A space-variant filter was designed to improve signal-to-noise ratio (SNR) in individual positron emission tomography (PET) "activated minus control" images. The aim of this study was to avoid averaging of signals from grey matter (GM) with those from surrounding white matter (WM) occurring after the usual Gaussian smoothing. The filtered images were obtained by solving the heat diffusion equation with a non-constant diffusion coefficient, chosen in order to restrict inter-region smoothing. Several diffusion coefficient maps calculated from a segmented magnetic resonance (MR) image were tested. Monte-Carlo simulations were used to characterize anisotropic diffusion filtering (ADF), in terms of GM signal preservation and statistical properties.